Dear Alex:

You can develop grain size distributions with any image analysis system. Measuring intercept lengths is a more difficult procedure than measuring grain areas. I have attached a Power Point presentation showing examples of grain size distributions, from normal (Gaussian) to bi-modal. It is best to ignore extremely small grains (only a couple of pixels per grain). Have fun!

George

Alex Gupta Yes, there's a lot of work to do for quantitative statistical validity. For a standard error on the mean of 1% you'll need a total of 10000 grains measured...

Hi Alan, thank you very much for your response. Could you please explain the rationale behind the 1 % standard error figure? In the papers I have read so far, the authors make a distribution based upon a single image, similar to the one I uploaded. Could you please refer me to a publication which utilizes such a large sample set? When I mentioned that I am tasked with analyzing 100 images, I meant 100 different thin films with different processing conditions.

Thank you.

Alex Gupta Standard statistics. Here's a quote from NBS authors in 1987 (the year it changed its name to NIST):

“S(tandard error) is proportional to N-1/2 where N is the total number of particles measured…This consideration implies that image analysis may require the analysis of on the order of 10000 images to obtain a satisfactory limit of uncertainty” (p718, paragraph 1) in:

A L Dragoo, C R Robbins, S M Hsu et al “A critical assessment of requirements for ceramic powder characterisation” Advances in Ceramics Vol 21 Ceramic Powder Science (1987). The American Ceramic Society Inc. (p711 - 720)

More detailed information is available in this webinar and also in the 1/2 day sampling course I do at Pittcon every year:

June 13th, 2019 Sampling for Particle Size Analysis Estimation of Standard Error

https://www.brainshark.com/malvern/vu?pi=zFZzAbWMKz5chz0

Alex Gupta 2 more references to statistical theory in this area:

• C J Brookes, I G Betteley, A M Loxston “Mathematics and Statistics for Chemists” John Wiley & Sons page 266 (1966)
• H Lucas “Statistical Methods” Butterworths page 77 (1970)

Plus an attached invited paper from WCPT7 in the Brian Scarlet Memorial session.

Alan F Rawle , thank you for the references!

Dear Alex Gupta,

ImageJ is in my opinion the correct tool. You are getting problems because of the quality of the image. There are two types of SEM images in publications:

1) Pleasant to the eye

2) Useful for image analysis

Your image is type 1) because you use around 40 gray values for your structure. You need to enhance the contrast while taking the image, not in post processing. This way you get more information of the sample.

It is ok to have oversaturated pixels and dark ones in the image, as long as the area of interest spans the whole gray value scale.

Kind regards,

Sascha

Sascha Wolter

Yes, Image J is extensively used - it's wonderful freeware. Issues will revolve around thresholding prior to binarization but Image J can deal with a 'moving background'.

Clearly, the original image taken cannot be improved, so it's vital that this is of the highest quality.

Dear Alex:

You can develop grain size distributions with any image analysis system. Measuring intercept lengths is a more difficult procedure than measuring grain areas. I have attached a Power Point presentation showing examples of grain size distributions, from normal (Gaussian) to bi-modal. It is best to ignore extremely small grains (only a couple of pixels per grain). Have fun!

George

George Frederic Vander Voort

IMHO, 2 pixels is way too low and down at the noise level... I use the advice of Eric Pirard (2010):

“My practical experience recommends me to use:

• Min 25 pixels to properly estimate size
• Min 250 pixels to properly estimate an aspect ratio (not a shape factor)
• Min 2500 pixels to estimate roughness (with the best method, certainly not with fractals and such things)"

Alan:

Those are good suggestions. I dump off the really small area values, but I do not bother to see how many pixels are present. If you include the "noise" from very small detected :grains", you will pump up the skew.

George

George Frederic Vander Voort

Yes, the harder you look then the more you see.

Alan:

So true! I published a short paper on my approach to measuring grain size distributions (attached).

George

The discussion is good and I would like to thank everyone for the scientific materials provided. MountainsMap specialized software is analyzed for SEM images provided. you can download it from the link below:

https://www.digitalsurf.com/,

Good luck in research Yours sincerely Emil Yankov

Thanks for the good question and the scientific materials provided by everyone. I published a research paper on my approach to measuring the average grain size (d). It is essential to determine the size of each grain for obtaining the grain size distribution. You can calculate the size of each grain according to my approach, and then conducte statistical analysis. Finally, the grain size distribution can be determined. You can download the paper from the following link:

https://dx.doi.org/10.1088/2053-1591/ab5384

I hope to help you.

Dear Peng Jia:

I would not recommend doing a grain size distribution based on the average grain size, d. If you are referring to d, the square root of the grain area, that is implying that grains are cubes in 3D. I did not read your article. ASTM E 112 defines the average grain area, d, as the square root of A, the mean grain area (the mean grain area is 1 divided by N sub L or P sub L. The mean area of the grains can be used to directly calculate the ASTM grain size number. But, you cannot make that calculation using d. Did you look at either of my two attachments above?

Dear Prof. George Frederic Vander Voort:

I am very appreciate for your advice.